Question

=Word problemining the area between two concentric canciesMeaghan vEA flower garden is shaped like acides amis 38 yd. A ring-shaped path goes around the garden. The width of the path is 6 yd.The garden is going to cover the path with sand. If one bag of sand can cover 4 yd, how many bags of sand does the gardener need? Note that and comesonly by the bag, so the number of bags must be a whole number. (Use the value 3.14 for 2)

Answer 1

Step-by-step explanation:

Given:

Diameter of the small circle = 38 yd

Diameter of the big circle = 38 yd + 2(6) yd = 50 yd

To find the area of the circle, we use the formula:

A= (πD^2)/4

where:

A=Area

D=Diameter

π=3.14

First, we find the area of the small circle.

`\begin{gathered} A=((3.14)(38yd)^2)/(4) \\ \text{Calculate} \\ A=1133.54yd^2 \end{gathered}`

Next, we find the area of the big circle.

`\begin{gathered} A=((3.14)(50yd)^2)/(4) \\ \text{Calculate} \\ A=\text{ }1962.5yd^2 \end{gathered}`

Then, the area of the path is:

Path Area = Area of the big circle - Area of the small circle

=1962.5 yd^2 - 1133.54 yd^2

=828.96 yd^2

So the total number of bags:

n=828.96/4 = 207.24 = 208

Therefore, the number of bags is 208.